Showing f(S ∩ T) ⊆ f(S) ∩ f(T) for set function

[Az-m-b]

Ex 36, p 147.

Let f be a function from the set A to the Set B. Let S and T be the subset of A. Show that

b) f(S $$\cap$$ T) $$\subseteq$$ f(S) $$\cap$$ f(T).

Thanks.

 

[llello]

Any time you prove subset relations, you have to show that any element of the subset is an element of the parent set. Let x be an element of the subset, show it is in the parent set.